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A pendulum of length l=5.0m attached to the ceiling carries a ball of mass 10.0 kg. The ball (a massive bob) is moved from its stationary equilibrium position to some distance such that the pendulum’s rope makes an angle of 60∘∘ with the vertical and then is released and allowed to swing. What is the total energy of the system at the moment of release in joules? Assume the lowest point on the trajectory to be y=0. (Do not include unit in answer)

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Respuesta :

Answer:

    Em₀ = 245 J

Explanation:

We can solve this problem with the concepts of energy conservation, we assume that there is no friction with the air.

Initial energy the highest point

        Em₀ = U

        Em₀ = m g h

The height can be found with trigonometry

The length of the pendulum is L and the length for the angle of 60 ° is L ’, therefore the height from the lowest point is

         h = L - L’

         cos θ = L ’/ L

         L ’= L cos θ

          h = L (1 - cos θ)

We replace

         Em₀ = m g L (1- cos θ)

Let's calculate

         Em₀ = 10 9.8 5.0 (1 - cos 60)

         Em₀ = 245 J

Cricetus

The total energy of the system will be "245 J".

Energy conservation

According to the question,

Angle = 60°

Mass = 10.0 kg  

Let,

With the air, there is no friction. And by using Energy of conservation, we get

→ Em₀ = U

          = mgh ...(equation 1)

Here,

h = L - L'

and,

Cosθ = [tex]\frac{L'}{L}[/tex]

     L' = L Cosθ

     h = L (1 - Cosθ)

By substituting the value of "h" in "equation 1", we get

→ Total energy, Em₀ = mgh(1 - Cosθ)

By substituting the values,

                                  = 10 × 9.8 × 5.0 (1 - Cos60°)

                                  = 245 J

Thus the above answer is correct.

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